Fair enough. My thinking when merging the two concepts was that the distinction doesn’t matter for any of the theory really. We don’t need to reason about “all possible linearizations whose diagram is at least as good as one gets when grouping these transactions together”, we can reason about the groupings directly.
And from an implementation perspective, specializing a grouping to a full linearization is trivial, and does not worsen the diagram, so any procedure that yields a grouping whose diagram is desirable can be trivially turned into one that produces a full linearization with an equal or better diagram.
That said, I agree it’s probably better to just have a different term altogether, because \{\varnothing, G\} indeed doesn’t convey any actual order. “escalating grouping” is a bit long though, and more an “implementation detail” than functional describing what it accomplishes. How about calling it a guide for a cluster? A linearization would then be a full guide, or if we keep thinking of linearizations as lists, they’d be isomorphic with full guides.
Well the result is still only a partial ordering on the elements (which needs to be combined with the partial ordering imposed by the graph structure).
That’s unnecessary because L' necessarily includes \varnothing as element.
Indeed.